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Giải bài tập 2 trang 78 SGK Toán 9 tập 2 - Cánh diều

Cho tứ giác ABCD nội tiếp đường tròn. Tính số đo các góc còn lại của tứ giác đó trong mỗi trường hợp sau: a) (widehat A = 60^circ ,widehat B = 125^circ .) b) (widehat B = 95^circ ,widehat C = 67^circ .) c) (widehat C = 75^circ ,widehat D = 115^circ .) d) (widehat D = 103^circ ,widehat A = 117^circ .)

Tổng hợp Đề thi vào 10 có đáp án và lời giải

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Đề bài

Cho tứ giác ABCD nội tiếp đường tròn. Tính số đo các góc còn lại của tứ giác đó trong mỗi trường hợp sau: a) \(\widehat A = 60^\circ ,\widehat B = 125^\circ .\) b) \(\widehat B = 95^\circ ,\widehat C = 67^\circ .\) c) \(\widehat C = 75^\circ ,\widehat D = 115^\circ .\) d) \(\widehat D = 103^\circ ,\widehat A = 117^\circ .\)

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Lý thuyết: Trong một tứ giác nội tiếp đường tròn, tổng 2 góc đối diện bằng \(180^\circ \).

Lời giải chi tiết

Vì tứ giác ABCD nội tiếp đường tròn nên tổng 2 góc đối bằng \(180^\circ \), do đó ta có: \(\widehat A + \widehat C = 180^\circ ,\widehat B + \widehat D = 180^\circ .\) a)     \(\widehat A + \widehat C = 180^\circ \) suy ra \(\widehat C = 180^\circ  - \widehat A = 180^\circ  - 60^\circ  = 120^\circ .\) \(\widehat B + \widehat D = 180^\circ \) suy ra \(\widehat D = 180^\circ  - \widehat B = 180^\circ  - 125^\circ  = 55^\circ .\) b)    \(\widehat B + \widehat D = 180^\circ \) suy ra \(\widehat D = 180^\circ  - \widehat B = 180^\circ  - 95^\circ  = 85^\circ .\) \(\widehat A + \widehat C = 180^\circ \) suy ra \(\widehat C = 180^\circ  - \widehat A = 180^\circ  - 67^\circ  = 113^\circ .\) c)     \(\widehat A + \widehat C = 180^\circ \) suy ra \(\widehat A = 180^\circ  - \widehat C = 180^\circ  - 75^\circ  = 105^\circ .\) \(\widehat B + \widehat D = 180^\circ \) suy ra \(\widehat B = 180^\circ  - \widehat D = 180^\circ  - 115^\circ  = 65^\circ .\) d)    \(\widehat B + \widehat D = 180^\circ \) suy ra \(\widehat B = 180^\circ  - \widehat D = 180^\circ  - 103^\circ  = 77^\circ .\) \(\widehat A + \widehat C = 180^\circ \) suy ra \(\widehat C = 180^\circ  - \widehat A = 180^\circ  - 117^\circ  = 63^\circ .\)

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